Step one was to open up the texture and copy the hair parts over the empty areas of the texture which were filled with skin color, even near the hair. That reduced it, but it still showed up with AA on.
I next forced skin textures to only have a few mipmaps, to make sure that wasn't the issue. Reduced, but still happened.
When I dumped the character model as a .x file and loaded it in Unwrap3d, I saw that the 3 submeshes of the texture were not all in the [0..1] range, two were translated, one left, and one down.
I remembered that issue, and realized that to 'fix' it, I had set the texture wrap mode on the characters to wrap. Turns out, the bottom of the char's skin texture was skin colored ( legitimately, for the hands ), so the wrapping was kicking in on near-horizontal triangles, bringing in the nice bright skin color when the texture wrapped around vertically.
I can't easily fix the character models, our last character artist flaked out a while ago and is not returning our e-mails, so I needed to fix it up on loading.
That caused me to go back into the character animation code to add code to bring UV coords into [0..1] range when first loading. While in that code, I realized that I could probably speed up things a bit by not copying the texcoords down every frame into the cached vertex array, but only do it once when fixing things up.
It did speed things up a bit, so then I experimented with not updating the normals and tangents every frame, and that gave a nice boost, too, so I added code to only animate the normals and tangents every few frames. Looks the same, and runs much better. It's actually a single counter for all submeshes, so the more characters on screen, the less often it's run.
Now the canyon level, with 7 chars on screen, plus corpses, is running almost 50% faster than before, and no more skin artifacts.
Here is a shot of my weak work-in-progress DNA-like cloning effect.